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Automated mutual induction proof in separation logic

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Formal Aspects of Computing

Abstract

We present a deductive proof system to automatically prove separation logic entailments by mathematical induction. Our technique is called the mutual induction proof. It is an instance of the well-founded induction, a.k.a., Noetherian induction. More specifically, we propose a novel induction principle based on a well-founded relation of separation logic models. We implement this principle explicitly as inference rules so that it can be easily integrated into a deductive proof system. Our induction principle allows a goal entailment and other entailments derived during the proof search to be used as hypotheses to mutually prove each other. This feature increases the success chance of proving the goal entailment. We have implemented this mutual induction proof technique in a prototype prover and evaluated it on two entailment benchmarks collected from the literature as well as a synthetic benchmark. The experimental results are promising since our prover can prove most of the valid entailments in these benchmarks, and achieves a better performance than other state-of-the-art separation logic provers.

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Acknowledgements

We would like to thank the anonymous reviewers of the Formal Aspect of Computing journal for the careful reading and the constructive comments on our work. The first author wishes to thank Dr. Alwen Fernanto Tiu and an anonymous reviewer of LICS 2018 for the suggestion of using the term matching, instead of the term unification, when describing the induction hypothesis application. This research is partially supported by an NUS research Grant R-252-000-553-112 and an MoE Tier-2 Grant MOE2013-T2-2-146.

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Authors and Affiliations

  1. Department of Computer Science, School of Computing, National University of Singapore, Singapore, Singapore

    Quang-Trung Ta, Siau-Cheng Khoo & Wei-Ngan Chin

  2. Department of Computer Science, Stevens Institute of Technology, Hoboken, USA

    Ton Chanh Le

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  1. Quang-Trung Ta
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  2. Ton Chanh Le
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  3. Siau-Cheng Khoo
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  4. Wei-Ngan Chin
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Correspondence to Quang-Trung Ta.

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Connie Heitmeyer, Ana Cavalcanti, John Fitzgerald, and Stefania Gnesi

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Ta, QT., Le, T.C., Khoo, SC. et al. Automated mutual induction proof in separation logic. Form Asp Comp 31, 207–230 (2019). https://doi.org/10.1007/s00165-018-0471-5

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